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An approach for formally verifying the safety of automated vehicles is proposed. Due to the uniqueness of each traffic situation, we verify safety online, i.e., during the operation of the vehicle. The verification is performed by predicting the set of all possible occupancies of the automated vehicle and other traffic participants on the road. In order to capture all possible future scenarios, we apply reachability analysis to consider all possible behaviors of mathematical models considering uncertain inputs (e.g., sensor noise, disturbances) and partially unknown initial states. Safety is guaranteed with respect to the modeled uncertainties and behaviors if the occupancy of the automated vehicle does not intersect that of other traffic participants for all times. The applicability of the approach is demonstrated by test drives with an automated vehicle at the Robotics Institute at Carnegie Mellon University.